Consider a simple public good economy with three people and two goods: one public (x) and one private (y). Assume that one unit of public good can be produced with one unit of private good. Person 1's utility function is u₁(x,y) = logx + y₁, Person 2's utility function is u:(x,y) = 2logx + y₂, and Person 3's utility function is us(x,y) = 3logx + ys. a. (5 points) Find the optimal output of the public good by using Samuelson condition. b. (15 points) Find the tax shares by using Wicksell-Lindahl mechanism. c. (10 points) Comment on the efficiency and incentives properties of the Wicksell-Lindahl mechanism.